Sales forecasting for retail stores using hybrid neural networks and sales-affecting variables

Sales forecasting using machine learning

Recent machine learning (ML) methods help vendors forecast sales using event-based and contextual data, aiding inventory and profit management (Beese & Fahse, 2023). Although no model guarantees perfect accuracy, combining approaches and continuous tuning improves performance. Classical methods like ARIMA and Seasonal Autoregressive Integrated Moving Average (SARIMA) rely on statistical smoothing and are widely used for market-level forecasts (Eglite & Birzniece, 2022). However, global models such as RNNs, enhanced with covariates (e.g., time, price, events), offer better accuracy in handling interrelated time series, with performance gains of 1.76% MRMSSE and 6.47% MMASE (Ramos & Oliveira, 2023). Comparative evaluations show ML methods, including ANNs, outperform traditional approaches, especially when integrating both endogenous and exogenous variables (Martins & Galegale, 2023).

Further analysis of models like Random Forest, Linear Regression, XGBoost, and Keras DNNs shows prediction accuracy improves with product attributes and customer information (Rajasree & Ramyadevi, 2024). In fashion retail, deep neural networks (DNNs) combined with data mining were used to forecast new item sales based on historical patterns and expert input (Loureiro, Miguéis & Da Silva, 2018). Using separate seasonal datasets and grid search tuning, models achieved over 67% R². This suggests future research should integrate richer variables and external factors for improved sales forecasting outcomes.

Sales forecasting using artificial neural network

Recent ANN variants have enhanced retail sales forecasting accuracy. One study showed that integrating macroeconomic indicators like Consumer Price Index (CPI), Inventory Control System (ICS), and unemployment rates into ANN models significantly improved prediction performance (Haque, 2023). This highlights the importance of including broader economic variables to better reflect market dynamics. To address the limitations of traditional forecasting methods such as long execution time and low accuracy Zhao, Tian & Wang (2023) introduced the QLBiGRU model, combining Q-Learning and bidirectional gated recurrent unit (BiGRU), achieving better performance through automatic parameter optimization.

Intermittent sales, marked by irregular order arrivals, pose challenges for prediction. To address this, Ahmadov & Helo (2023) proposed a DNN with multi-layered architecture capable of capturing complex patterns, improving forecasting accuracy by up to 35% compared to classical models like ARIMA and Croston’s method. Using data from 17 sellers and 3,000 orders, the study validated DNN’s applicability across diverse retail environments. In supply chain forecasting, a hybrid SVM and ANN approach was applied for the food retail sector to predict future demand (Hussain & Haroon, 2018).

Another model by Silva et al. (2021) employed Ensemble Empirical Mode Decomposition (EEMD) with Bayesian Regularization ANN, Cubist Regression, and SVR. The model decomposed historical sales into intrinsic components and trained them individually using BRNN, Cubist, and SVR with a Radial Basis Function kernel. The ensemble results EEMD–BRNN, EEMD–CUBIST, and EEMD–SVR proved highly effective for daily sales forecasting with MAPE as low as 18.85.

Customer sentiment also impacts sales outcomes. A study by Biswas, Sanyal & Mukherjee (2023) analyzed reviews from Amazon (https://www.amazon.in/) and Snapdeal (https://www.snapdeal.com/) using ANN and IBM SPSS (IBM Corp., Armonk, NY, USA) (Al-Imam, 2019). Sentiments classified by a 1–5 scale influenced the sales forecast model, showing the impact of customer feedback. The authors suggested extending the model to include demographic variables and integrate both online and offline feedback for improved predictions.

Caglayan, Satoglu & Kapukaya (2020) used ANN for sales forecasting in a Turkish retail chain by analyzing historical sales, pricing, promotions, customer footfall, and weather. The model identified optimal network architecture and achieved reliable forecasting. Regression analysis was also applied for comparison. This multi-source data integration showed the importance of contextual factors in accurate forecasting.

Sales forecasting using LSTM and ensemble learning

Ensemble methods are vital for improving sales forecasting accuracy by combining multiple models to offset individual biases. Techniques like voting regressors have shown notable performance gains, particularly with large datasets (Alice, Andrabi & Jha, 2023). A study using XGBoost, LGBM, and CatBoost demonstrated their effectiveness in retail forecasting, emphasizing their unique strengths (Alice, Andrabi & Jha, 2023). Accurate forecasts are essential for optimizing supply chains and enhancing customer satisfaction (Kilimci et al., 2019). Traditional models often struggle with complex sales data, prompting exploration into deep learning (DL) techniques.

To address data limitations, deep transfer learning has been applied, where knowledge from one task improves forecasting on another with limited data (Erol & Inkaya, 2023). Two ensemble DL methods bagged and stacked were introduced. Bagging combines predictions from long short-term memory-transfer learning (LSTM-TL) models trained on different data subsets to reduce variance. Stacking merges multiple LSTM-TL outputs through a higher-level model to capture complex relationships (Erol & Inkaya, 2023). The stacked method showed superior accuracy compared to bagging due to its deeper learning capacity.

These techniques help mitigate overfitting and improve model generalization by leveraging diverse architectures. Another integrative ensemble model combined weighted XGBoost, ARIMA, and Holt-Winters to reduce overfitting and information leakage (Aun et al., 2022).

Additional studies also favor ensemble learning. Sajawal et al. (2022) showed that XGBoost outperformed traditional regressors, with MAE = 0.516 and RMSE = 0.63. Similarly, Kumar et al. (2023) found that tuning XGBoost with RandomizedSearchCV yielded better results than multiple classic ML models.

Sales forecasting using CNN and hybrid neural networks

A hybrid model was proposed to improve demand forecasting per SKU by selecting the best two among five regression methods (LR, PR, RF, SVR, GBR), achieving a MAPE of 7.74% (Taparia et al., 2024). However, it focused mainly on price-related features and lacked broader sales influencers like holidays or weather. Deep learning integration using CNN and LSTM has also been explored through stacked and parallel hybrid models, achieving MAPEs of 14.15% and 14.76% respectively on retail data (Castro Moraes, Yuan & Chew, 2024), though limited by univariate inputs.

Other hybrid strategies combine trend and residual learners (e.g., LR, ElasticNet, RF, XGB) to boost accuracy, such as the Lucy model which supports model saving for efficient reuse (Tran, Huh & Kim, 2023). Another approach embedded exponential smoothing into a GRU-CNN-LSTM framework (ATES) to handle seasonal data, improving accuracy over baselines like WaveNet and TFT (Efat et al., 2024). This model leveraged both sequence modeling and clustering, trained on multi-year sales data.

Hybrid ARIMA-BPNN models have also incorporated content popularity (from Google search data) into sales forecasts for magazine retail, outperforming traditional models through combined trend and nonlinear pattern learning (Omar, Hoang & Liu, 2016).

Recent work in retail supply chains recommends multivariate models that include store location, weather, and promotions. A GRU model optimized via Grid Search, applied to Rossmann store data, showed stronger forecast accuracy, although it lacked store closure information (Qureshi et al., 2024).

Collectively, studies show that while many AI models (ANN, ML, LSTM, CNN, RNN, hybrids) exist for retail forecasting, most use artificial or incomplete real datasets that ignore crucial variables like environmental or demographic data. Since no single model handles both spatial and temporal dependencies well, there is a clear need for hybrid models that integrate these factors without compromising user privacy. Recent comparisons confirm CNN-BiLSTM hybrids outperform standalone models like ARIMA, CNN, or LSTM in terms of RMSE and MAE (Joseph et al., 2022). Similarly, Ahmed et al. (2024) found CNN-LSTM hybrids more robust and accurate than individual DL architectures, offering a balance of accuracy and interpretability without requiring large datasets or excessive tuning.

By analysing the solutions provided in the available literature above, we have come up with a novel and optimal solution based on the hybrid (CNN and LSTM) model and by considering some environmental and demographic variables, to improve forecasting sales. In Table 1, some research studies are listed that we found closest to the sales forecasting domain and are using AI models to improve sales forecasting accuracy. A comparative analysis of these research studies is done on the basis of MAPE value, as we will be using MAPE as our base evaluation metric for comparing the results of our proposed solution with these existing research studies.

CNN model

CNNs, while originally developed for image processing, have also shown promise in identifying patterns within structured data. Their strength lies in modeling complex, non-linear relationships between static input features such as promotions, store locations, or environmental indicators and sales outcomes. Although CNNs can detect local trends in time series data, they are limited in capturing long-term temporal dependencies due to the absence of a recurrent structure. In our proposed model, CNN is used to extract short-term feature patterns that contribute to sales variation.

LSTM model

LSTM networks are well-suited for modeling sequential data and capturing temporal dependencies, such as seasonality or recurring demand shifts in sales. They retain information across time steps, allowing the model to learn from past patterns that influence future outcomes. However, LSTMs can be computationally intensive and sensitive to noise if data is sparse or unrefined. In our hybrid model, LSTM complements CNN by addressing the temporal aspects of sales forecasting, particularly where historical trends and event-driven fluctuations are significant.

Environmental and demographic factors

Retail sales forecasting is influenced by both internal and external variables. Beyond the core fields (date, sales, and open/closed status) in our Kaggle dataset (ITEXPERTFSD, 2024), we incorporated additional environmental and demographic factors:

(A) Environmental Variables

Based on sales drops observed on certain days, we matched weather data from the city (Crossing, 2024) and defined:

• EffectiveRain: Days with precipitation $\ge$20 mm were labeled as rainy. These often corresponded with decreased sales.

• EffectiveTemperature: Days with temperatures $\ge$40 °C were marked as hot days, also associated with reduced customer activity.

(B) Demographic Variables

Sales fluctuations also aligned with specific calendar or social events. We categorized them as:

• PositiveEvents: Includes holidays, salary days, store promotions, and national/religious occasions typically boosting sales.

• NegativeEvents: Includes mid-week days (notably Wednesday), protest days, and partial closures linked with lower sales activity.

Proposed model and data overview

To effectively capture both temporal patterns and short-term fluctuations in retail sales, we employed a hybrid CNN-LSTM architecture (Fig. 1). LSTM components handle sequential dependencies such as trends and seasonality, while CNN layers help detect local patterns like sales spikes due to promotions or events. This complementary structure improves forecast precision, especially in volatile sales environments.

The model pipeline begins with data acquisition, followed by preprocessing and feature extraction. After transformation, inputs pass through CNN and LSTM layers sequentially, with the final dense layer producing the sales forecast. The model’s performance is evaluated using MAE, RMSE, and MAPE metrics.

Data collection and analysis

We used a publicly available Kaggle dataset containing 6 months of daily sales data from a retail store in Faisalabad, Pakistan (ITEXPERTFSD, 2024). To enrich the dataset, we integrated external demographic and environmental variables sourced from local public data.

• Daily Sales Data: Includes total daily sales figures for the store.

• Demographic Factors: Includes events such as holidays, promotions, salary days, protests, and partial closures that influence consumer activity.

• Environmental Factors: Incorporates temperature and precipitation data to capture weather-related impacts on store traffic and sales.

These variables enable the hybrid model to learn from both internal and external sales influencers, improving its ability to forecast demand under varying real-world conditions.

Tools and technologies and computing infrastructure

The proposed CNN-LSTM hybrid model was developed and tested using Python and standard machine learning libraries on Google Colab, which offers cloud-based GPU acceleration. The tools used supported data preprocessing, model training, evaluation, and visualization. Key frameworks included TensorFlow/Keras for deep learning and Scikit-learn for preprocessing and performance metrics. The full software stack and system specifications are summarized in Table 2.

Baselining models for comparison

To assess the performance of the proposed model, we implemented two baseline models (LSTM & CNN) for comparison. Each model was trained and evaluated on the same dataset using standardized preprocessing techniques. Performance was measured using common regression metrics including MAE, RMSE, and MAPE.

By comparing the proposed hybrid model’s results against these baseline models, the study demonstrates a significant improvement in predictive accuracy, especially when external influencing variables are included. This comparative analysis provides stronger support for the effectiveness of the hybrid neural network model in retail sales forecasting.

Data pre-processing

Data preprocessing is a crucial step before feeding the data into the models. Our dataset consists not just of daily sales data but also some other demographic and environmental data related to the retail store location. So, the following preprocessing steps were carried out to make data suitable for our model to forecast sales accurately:

• Handling Qualitative Data: Qualitative data like holidays, national events/festivals and stores open/closure/partially closed, hot weather, effective rain and protests are required to be converted into numerical format. It helps train the model to get the best forecasting results.

• Normalisation/Scaling: The data was normalised using Min-Max Scaling to ensure that all input features are within a similar range, which improves model performance.

• Feature Engineering: Additional features such as (lagged sales values, moving averages, holiday flags) were created to capture trends and seasonality. The time series was also decomposed into (trend, seasonal, and residual components) for better model interpretation.

• Data Availability: The final dataset consisting of sales data obtained from Kaggle, publicly available weather data and public holidays data is consolidated together as one Dataset (CSV file), which is available at Mansur (2025).

Proposed model implementation details

After analyzing the sales data, we implemented a hybrid CNN-LSTM model to capture both local (short-term) and global (long-term) patterns. The model begins with 1D convolutional layers that apply filters across the time dimension to detect temporal features such as sales spikes, dips, and short-term trends often influenced by promotions, holidays, or weather events. These filters help extract spatial patterns from time-series data by sliding over sequences of input shaped as (timesteps, features). The convolutional output is then passed to LSTM layers, which capture sequential dependencies and long-term trends. As detailed in Table 3, the dataset includes multiple external variables such as weather thresholds and event indicators which enhance the model’s ability to recognize dynamic influences on sales behavior.

The hybrid CNN-LSTM model was fine-tuned through empirical testing to balance performance and complexity. For the CNN component, we used 64 filters with a kernel size of 4 and ReLU activation to extract meaningful short-term patterns from the 6-month sales dataset. A MaxPooling1D layer with a pool size of 2 was applied to reduce dimensionality while retaining dominant features.

The output from the CNN layers was passed to a single LSTM layer with 50 units to capture temporal dependencies such as trends and seasonality. A fully connected dense layer followed, mapping extracted features to the final sales prediction. The output layer used a single neuron with linear activation to produce the forecasted value.

Training was conducted using the Adam optimizer and MSE as the loss function. We trained the model for 150 epochs with a batch size of 32, and applied a 10% validation split to monitor performance. Dropout and additional stacked LSTM layers were omitted after experimentation showed that a single-layer configuration yielded stable and accurate results.

All selected hyperparameters are summarized in Table 4, based on manual tuning and performance evaluation using metrics such as MAPE and RMSE.

Model training

The model is trained using the training dataset, where historical sales data is split into sequences. Our model is trained for 150 epochs with early stopping based on validation loss to avoid over-fitting. We have tried the model with different epoch values to find an optimal number where the model performs best and overcomes under-fitting and over-fitting successfully. Results for different epoch values we tried are summarised in Table 5, where we can see that the model learns from these sequences to predict better future sales with MAPE 4.16%, for epochs value of 150. The input sequence length was set to 32 days to capture recent trends.

Analysis of solution evaluation and testing

We have evaluated our proposed hybrid model using various performance metrics to assess forecasting accuracy. The dataset was split into training and test sets using an 80–20 ratio. The following metrics were used for evaluation and analysis:

• MAE: Measures the average magnitude of the errors in a set of predictions.

  (1) $$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{n}\sum _{i=1}^n|y_i-{\hat{y}}_i|$$

• RMSE: Gives more weight to large errors, highlighting model performance on outliers.

  (2) $$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{n}\sum _{i=1}^n{(y_i-{\hat{y}}_i)}^2}$$

• MAPE: Useful for evaluating the percentage accuracy of the forecast compared to actual values.

  (3) $$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}=\frac{1}{n}\sum _{i=1}^n\left|\frac{y_i-{\hat{y}}_i}{y_i}\right|\times 100$$

Challenges and limitations

Since the start of the implementation phase for finding the optimal sales forecasting model, we have encountered multiple challenges which were resolved as we proceeded with more investigation and analysis of the dataset.

Spikes in sales data

The LSTM model is suitable for time series data forecasting and finds out the points where the behaviour is entirely different. Therefore, after analysing the sales data and passing it through the LSTM sales forecasting model, we came to know that our sales dataset has spikes (increases or decreases in sales amount) on some specific days of the month. So, after conducting further investigation and considering the demographic and environmental factors of the store location, we found out that sales numbers spiked due to the presence of these factors, like having more sales on a holiday or promotion day and fewer sales on a rainy day. Figure 2, shows a snapshot of the spikes in the original sales data. On the x-axis we have dates in increasing order and on the y-axis we have sales in PKR.

Ethical considerations

The dataset used in this study is publicly available from Kaggle (ITEXPERTFSD, 2024), and contains no personally identifiable information (PII). To ensure privacy, the store identity is anonymized, and no efforts were made to de-anonymize or link data to external sources. As no human subjects were involved, formal IRB approval was not required. All data handling adhered to principles of accuracy, reliability, and integrity.

Model findings and performance evaluation

The performance of the hybrid CNN-LSTM model was evaluated using standard metrics such as MAE, RMSE, and MAPE as shown in Table 7, which are commonly used to assess the accuracy of time-series forecasting models.

• MAE: The MAE value of 11,165 indicates the average magnitude of the forecasting error in terms of actual sales units. This suggests that, on average, the predicted sales values deviate from the actual sales by approximately 11,165 units.

• RMSE: The RMSE value of 26,200 reflects the overall error magnitude with more weight given to larger deviations. Although slightly higher than MAE, this value emphasises that larger forecasting errors occur occasionally but are relatively infrequent.

• MAPE: The MAPE value of 4.16% indicates that the model’s predictions, on average, are off by only 4.16% of the actual sales values. This percentage is quite low, demonstrating the model’s high accuracy and efficiency in forecasting sales over time.

Critical analysis and comparison

In this section, we critically analysed and compared the performance of the proposed hybrid CNN-LSTM model. Also discussed are the benefits of the hybrid model and the impact of environmental and demographic factors.

Influence of environmental and demographic factors

We can find the collective impact of adding demographic and environmental factors by looking at the values of MAPE in Table 8.

Table 8:

Sales forecasting using demographic and environmental factors.

Dataset	MAE	RMSE	MAPE
1st run: with only sales data	21,667	39,216.71	8.02%
2nd run: sales data with environment factors	21,326	45,661	7.89%
3rd run: sales data with demographic factor	11,979	24,167	5.14%
4th run: sales data with environment and demographic factors	11,165	26,200	4.16%

DOI: 10.7717/peerj-cs.3058/table-8

When we run the proposed model with only univariate sales data, the MAPE value is 8.02%. In the second run, we modified our dataset and code by adding environmental factors like precipitation and temperature, the MAPE value is 7.89%. This reduction in error shows improvement in results, which proves that these variables are affecting sales forecasts and should be considered while forecasting future sales. In the third run, we removed environmental factors and added some demographic factors like store open/close/partially closed, promotions in sales, holidays, events and protests. We can see from the results that these factors or variables are more effective on sales and by considering these variables we can reduce the MAPE error to 5.14%. Then, finally, we ran our proposed model by considering all variables together. These factors contributed to the hybrid CNN-LSTM model achieving a low MAPE of 4.16%, indicating that the model’s predictive accuracy was notably enhanced by the inclusion of both demographic and environmental features. This integration of external variables made the model more versatile and responsive to the various dynamic influences on consumer behaviour, highlighting its effectiveness as a sales forecasting tool in complex, real-world conditions. The performance comparison between the first run (using only sales data) and the third run (incorporating demographic factors) as shown in Fig. 3, reveals a significant improvement in forecasting accuracy. As shown in the graph, the MAE dropped from 21,667 to 11,979 and the RMSE decreased from 39,216.71 to 24,167, indicating a substantial reduction in both absolute and squared error. Moreover, the MAPE improved from 8.02% to 5.14%, demonstrating better relative prediction accuracy. These improvements suggest that integrating demographic variables into the input dataset enhanced the model’s ability to capture patterns influencing sales behavior, leading to more reliable and accurate forecasts.

The most representative 30 entries from the 60-day forecast output of the model’s 4th run, along with corresponding actual sales, are shown in Table 9.

Table 9:

Sales forecast 4th run testing results.

Sr.#	Date	Forecast	Actual	Sr.#	Date	Forecast	Actual
1	20/07/2024	265,987	267,990	31	19/08/2024	204,762	202,740
5	24/07/2024	177,357	175,229	35	23/08/2024	216,116	220,167
10	29/07/2024	161,950	159,432	40	28/08/2024	183,005	177,850
12	31/07/2024	238,606	236,590	42	30/08/2024	212,852	210,000
14	02/08/2024	411,558	411,546	44	01/09/2024	492,786	492,061
16	04/08/2024	358,181	354,847	46	03/09/2024	271,233	269,059
18	06/08/2024	306,314	301,310	48	05/09/2024	345,141	371,018
20	08/08/2024	233,098	228,803	50	07/09/2024	245,036	321,005
22	10/08/2024	275,955	278,283	52	09/09/2024	219,303	221,824
24	12/08/2024	238,543	235,975	54	11/09/2024	228,333	203,174
26	14/08/2024	284,181	281,416	56	13/09/2024	197,255	165,445
28	16/08/2024	233,950	234,655	58	15/09/2024	198,471	308,632
30	18/08/2024	293,234	294,257	60	17/09/2024	278,710	284,303

DOI: 10.7717/peerj-cs.3058/table-9

Actual and forecasted values are compared and plotted graphically as shown in Fig. 4. On x-axis dates are in increasing order, whereas on y-axis sales are in PKR. We can easily see the difference between both actual and forecast values.

After applying our proposed sales forecasting model on the dataset consisting of 6 months of sales data with all demographic and environmental factors, we can infer that model performed well by looking at the forecasted values that are matching with the actual sale values. The results in Fig. 5 have shown that the applied forecasting model has successfully picked spikes in original sales values by getting trained with provided environmental and demographic factors.

In Fig. 6, training loss and validation loss values are plotted where the x-axis shows the epochs of the training process and the y-axis shows the loss value. We can see a continuous decrease in training loss indicates that the model is improving its ability to fit the training data and it is learning well during the training process. On the other hand, looking at the values for validation loss shows that the model does not fit well for any unseen data, hence memorising the training data but failing to generalise to new examples. The reason for this over-fitting is the presence of sales spikes in the dataset, which are forecasted very well by the model after we added the demographic and environmental factors specifically for our dataset. This concludes that the proposed model requires the dataset to have the appropriate factors accordingly and then be fed into the model.

Discussion on the results of different models on the same dataset

Based on our experiments, individual models such as ANN, CNN, and LSTM showed limited forecasting accuracy, even after incorporating external variables. Among them, LSTM performed better due to its ability to capture temporal patterns, but it still lacked spatial awareness.

The hybrid CNN-LSTM model, which combines convolutional feature extraction with temporal sequence modeling, showed a clear improvement. When demographic and environmental variables were integrated into this architecture, the model achieved a significantly lower MAPE of 4.16%, outperforming all baseline approaches.

These findings confirm that combining spatial and temporal learning in a hybrid framework, along with context-aware variables, substantially enhances sales forecast precision in retail environments.